AMRMHD3D.f

A Test of 3D Flux-Corrected Transport Solvers
for Ideal, Compressible Magnetohydrodynamics
with Adaptive Mesh Refinement

The first test of our adaptively refined MHD code is for problem size scaling with the number of processors. In this example, each of the processors holds between 41 and 61 blocks of 8x8x8 grid points, deployed on 4, 16, 32, 128, and 512 processors. Thus, the physical problem ranges approximately from 120K grid points on 4 PEs to 10.7M grid points on 512 PEs, as the number of grid refinement levels allowed increases from four to seven. This last run attained 11.7 GFlops on the T3E. The code scales very nearly linearly, and extrapolates to attain about 23 GFlops on a 1024-processor T3E. This compares with 45 MFlops on a single C90 processor for the four-level problem, or a speedup of more than 500 times on 1024 T3E processors.

The following graph shows the results of this scaled-problem test:

The second test is for a fixed problem size of 3.2M grid points using seven levels of refinement. The mesh is distributed as evenly as possible across the processors, so that the number of 8x8x8 grid blocks decreases from 49 per PE on the 128-PE partition down to 12 per PE on the 512-PE partition. This last run attained 9.9 GFlops, or 220 times the C90 performance. The per-PE performance on the T3E deteriorates noticeably as the number of PEs rises, with the problem size fixed, because the ratio of time spent communicating to that doing useful work increases significantly.

The following graph shows the results of this fixed-problem test:

The package of AMR routines with which the NRL MHD code was merged was written by Peter MacNeice, Kevin Olson, Clark Mobarry, Rosalinda de Fainchtein, and Charles Packer. Many helpful discussions with them during a cooperative development effort on this code are gratefully acknowledged. Thomas J. Clune of Cray also provided a number of helpful suggestions and ran several early test cases with the code-in-progress, for which he deserves thanks.

Point of Contact:
C. Richard DeVore
Naval Research Laboratory
Phone 202.767.2096
e-mail:devore@lcp.nrl.navy.mil